In the past few decades, nature-inspired computation has attracted more attention. Many real-world engineering optimization problems are substantially very complicated and quite difficult to solve . However, nature serves as a fertile source of concepts, principles, and mechanisms for designing artificial computation systems to tackle complicated computational problems. In nature, mouth brooding fishes employ their mouth as a barrier against the surrounding dangers threatening their children. MBF algorithm has been inspired by nature; it is based on the behavior and the distance of movement and dispersion of the children around the mother’s mouth. In the section of Mouth Brooding Fish Algorithm, and subsection of basic concepts, the initial and general concepts are developed from the natural behavior of the fish; MBF algorithm features, the way the concepts are manipulated within the algorithm; pseudo code discussion, coding comparison and discussion between MBF and well known PSO algorithm; and tuning parameters, the experimental process to determine which control parameters are robust or sensitive and perform suggestion for the users; are presented . In the section of Comparison with Advanced Algorithms, the efficiency of this algorithm is compared with the advanced algorithms (CMA-ES, JADE, SaDE, and GL-25), which have widespread applications in global optimization problems due to their advantage of accuracy and speed in obtaining global optima.
Sensitivity analysis is the experimental process by which we determine the relative importance of the various factors of a system. For every new meta-heuristics, we need to know how sensitive an approach is to its control parameters and which control parameters are robust/or sensitive. However, sensitivity analysis goes through a long process that could take away the main focus of paper from the main subject of proposed algorithm; therefore, this section introduces parameter tuning which is running the MBF algorithm with different settings on control parameters and tries to suggest the best setting for each type of problems .
2. Inspiration of Mouth Brooding Fish (MFO) Algorithm
Males are either dominant and territory-holding or subordinate and non-territorial; these phenotypes differ in coloration, reproductive, hormonal and metabolic states. Males can also reversibly switch between these social states depending on the social environment. (B) Females also differ in reproductive, hormonal and metabolic states . Sexually receptive gravid females will spawn with dominant males and then carry the developing fry in their mouths for ∼2 weeks (mouth brooding), which is a period of starvation, reduced ovarian growth and lower levels of circulating steroids. After releasing free-swimming fry, females undergo a recovery period characterized by ovarian recrudescence and increased feeding until they become gravid again and ready to spawn .
3. Mouth Brooding Fish (MFO) Algorithm
MBF algorithm has been inspired by the process of mouth brooding Fish life cycle. Like all other algorithms, MBF has a number of controlling parameters that are set by the user . These controlling parameters work like setting volumes that adjust the algorithm to the problem in order to reach a faster convergence and find the best possible answer. MBF algorithm has 5 controlling parameters which are determined by the user. These controlling parameters are the number of population of cichlids, mother’s source point (SP), the amount of dispersion the probability of dispersion, and mother’s source point damping. In order to choose the best possible values for the controlling parameters, one may consider the problem and the results of tuning parameters. Although we must assume the controlling parameters as a constant to make the MBF algorithm capable for comparing with CMAES, JADE, SaDE, and GL-25. MBF algorithm is a population-based algorithm; therefore, the number of population is one of the controlling parameters. The number of population shows that how many fish will go through the operation of solving a problem in Mouth Brooding Fish algorithm . The main base of Mouth Brooding Fish algorithm is the movements of cichlids around their mother and the e effects of nature or danger on these movements. MBF algorithm procedure is consisting of main parts in order to find the best possible results for the problems.
In nature, the marriage is one of the important operators that help the colony or population to converge through the best possible results. Although when it happens it does not always have good results. Mouth brooding fish allowed some of the best cichlids to marry in their population, therefore, in MBF algorithm by using a probability distribution or Roulette Wheel selection (i.e. members with higher points values have a higher chance) we select 1 pairs of parents from each cichlid. These newly born cichlids that have new position take the place of their parents in population and their movement would be zero . Before evaluating the newly born fish with fitness function we should check that the new position for the generated children is in the search space area.
3.1. Fish Breeding Strategies
The mouth brooding strategy involves the female carrying and guarding the fertilized eggs inside her mouth, an example of a species of fish that uses the mouth brooding strategy is Cyphotilapia Frontosa .
- A general description of this method
- Species variation
- Parental protection
- Offspring numbers
- Survival strategy
- Energy costs
3.1.1. A general description of this method
With mouth brooder’s the male and female will then start to circle each other. The female will lay one of her eggs and swim over it, the male will then swim over the egg and spray milt to fertilise it, then the female will pick up the fertilized egg. This procedure will repeat until all of the eggs have been fertilized and collected by the female. The female will then carry her brood in her mouth for around three weeks, then will release the fry and will protect and guard them until they become independent and can survive on their own. With the Frontosa Cichlid, the male will firstly leave his cave, making it look presentable to the female; the female will enter and lay her eggs on the spot that the male has cleared for her . The male will then fertilise the eggs, and the female will collect them in her mouth and guard and protect them there for around 28 days, until they are strong enough to be released .
3.1.2. Species variation
There are two different variations of mouth brooder’s. Some mouth brooders are ovophiles, this means that they pick up the fertilized eggs in their mouths and also carry their brood when they have hatched. Although, some mouth brooder’s are larvophiles, this means that they guard and protect their eggs until they hatch, and they then pick up the fry in their mouths and protect them . This can vary depending on the species but both methods require high amounts of energy from the female.
3.1.3. Parental protection
Mouth brooder’s provide parental protection and do in fact look after their brood. The eggs and the larvae are protected in the female’s mouth , which keep them sheltered from predators and will also will mean that they are more likely to survive, increasing the population of the species.
3.1.4. Offspring numbers
The brood size for Frontosa Cichlid’s is usually around 50 eggs, but mouth brooders in general can produce broods that range from 20-50 fry . They do not need to produce as many eggs as egg scatterer’s due to their higher success rate, and also due to the fact that they protect their young, giving them a better chance of survival .
3.1.5. Survival strategy
The female will take her fry back into her mouth if she spots any potential danger, and she will continue to due this until they become independent. This is the strategy which is used to aid the survival of the brood. This is a very successful method of ensuring their survival as the female is protecting and looking after the brood during their vulnerable stage, she makes sure that they are safe from predators and also puts herself at risk by protecting her fry . As her fry continue to grow in size, she will begin to take the strongest and biggest of the fry into her mouth first, if there are any signs of danger, this is to ensure that the fry with the better chance of surviving on their own are protected first. She does this as she will not have enough room in her mouth to protect all of her brood, so she must choose the ones that will strengthen the species (survival of the fittest), this method usually means that the weakest and smallest of the brood will be predated on .
3.1.6. Energy costs
The energy costs are very high with this strategy, this is due to the fact that the female has to exist without food, she also uses her energy to bring her fry to feeding ground and protect them whilst they feed, meaning she has to use a lot of her energy even when the fry are beginning to become independent.
3.2. Flow Chart of MBF Algorithm
4. Numerical Methods of Mouth Brooding Fish Algorithm
Mouth Breeding Fish Algorithm Optimization problem is given by ,
5. Applications of MBF Algorithm
- Anatomical measurements
- Signal processing 
- Feature selection
- Industrial problems
- Data center network 
- Power generation
6. Advantages of MBF Algorithm
- To overcome with these limitations, many scholars and researchers have developed several metaheuristics to address complex/unsolved optimization problems over the last past decades.
- As with buccal volume, residuals of measurements against volume revealed no consistent trends; ratios were therefore used for ease of interpretation .
- Among them, global optimization algorithms such as Genetic Algorithm (GA) Particle Swarm Optimization (PSO) differential Evolution Algorithm (DE) have received much attention and are widely used in many fields such as function optimization civil engineering signal processing classification and machine learning due to their advantages in obtaining global optima and their rapid convergence .
- The experimental process to determine which control parameters is robust or sensitive and performs suggestion for the users; are presented.
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